A method is described for directly calculating the partition function of a Lennard-Jones liquid from a single equilibrium computer simulation. The method is a special adaptation of cell theory. The partition function is essentially that of an Einstein crystal, but with assumptions rendering it appropriate for a liquid. The method addresses the three traditional shortcomings of cell theory: namely, how to calculate cell properties, include particle correlations, and account for the communal entropy. A molecular dynamics simulation provides all the necessary parameters to evaluate the partition function. These parameters are the average potential energy and average magnitude of the force acting on each particle. Free energies calculated from the partition function over a range of density and temperature give good quantitative agreement with results from perturbation theory and experiment. The cell properties also yield insight into liquid structure. Prospects for the usefulness of the method for more complex systems are discussed. (C) 2003 American Institute of Physics.